The invention relates to a method and an apparatus for controlling the fuel-air mixture delivered to an internal combustion engine. More particularly, the invention relates to the method of supplying supplementary air to the fuel-air mixture in dependence on operational conditions of the engine by sensing the aspirated air flow quantity and metering out supplementary air through a bypass air line in accordance therewith. The control pressure at the metering location is altered multiplicatively by a pressure control valve whose control pressure varies between two substantially individually constant pressures. In a known method of fuel mixture control, the oxygen content of the exhaust gases is determined and supplementary air is admitted in dependence on the oxygen content of the exhaust gas via a bypass valve. In this known installation, an electronic controller senses the throttle valve position and the rpm of the engine and executes a basic setting of the bypass valve. In addition, the bypass valve is set in dependence on the oxygen content of the exhaust gases. This type of control requires relatively expensive controllers and other apparatus. Furthermore, the position of the throttle valve can be used only in combination with the rpm signal or the induction tube vacuum to determine the amount of fuel-air mixture which is actually aspirated by the engine. Thus, this latter quantity, the magnitude of which must be well known for satisfactory control, is derived only from two separate measured values and is then processed to generate a control pulse for the bypass valve.